Hi!swetabh
ysinA=xsin(2B+A)
y/x =sin(2B+A)/sinA
applying componendo and dividendo we get
(y+x)/(y-x)=[sin(2B+A)+sinA]/[sin(2B+A)-sinA].............1
now put sinA =sin(A+B-B) and
sin(2B+A)=sin[B+(B+A)]in the eq1 and expand them as
sin(A+B-B)=sin(A+B)cosB-sinBcos(A+B) and
sin[B+(A+B)]=sinBcos(A+B)+sin(A+B)cosB. By doing this u will finally get
(y+x)/(y-x)=cotB/cot(A+B)
now cross multiply and u will get
(y+x)cot(A+B)=(y-x)cotB